{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "from random import *\n",
    "from sympy.abc import *\n",
    "from IPython.display import display, Math\n",
    "import handcalcs.render\n",
    "import numpy as np\n",
    "from sympy.physics.hydrogen import*\n",
    "def out(x,x_1=0,x_2=0,x_3=0,x_4=0,x_5=0,x_6=0,x_7=0,x_8=0,x_9=0,x_10=0,x_11=0):\n",
    "   if x==0:\n",
    "      return\n",
    "   if x_1==0:\n",
    "       display(Math(latex(x)))\n",
    "   else:\n",
    "       if type(x_1)==str:\n",
    "          display(Math(x_1+latex(x)))\n",
    "       else:\n",
    "           display(Math(latex(x)))\n",
    "   out(x_2,x_3)\n",
    "   out(x_4,x_5)\n",
    "   out(x_6,x_7)\n",
    "   out(x_8,x_9)\n",
    "   out(x_10,x_11)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$v_{t}=v_{0} \\sqrt{1+\\frac{t}{273.15}},v_0=331.45$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\sqrt{2} \\sqrt{\\pi} \\operatorname{erf}{\\left(\\frac{\\sqrt{2}}{4} \\right)}$"
      ],
      "text/plain": [
       "sqrt(2)*sqrt(pi)*erf(sqrt(2)/4)"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrate(exp(-x**2/8),(x,0,1))"
   ]
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "05a237592cd1f1c47d6da52b1c9e9cb4b6d7e67883224033955e685c2762c5fd"
  },
  "kernelspec": {
   "display_name": "Python 3.9.10 64-bit (windows store)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
